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curve #4496

y² + y = x³ − 619x + 8670

a-invariants: [0, 0, 1, -619, 8670]
c-invariants: [29712, -7491096]
rank (lower bound): ≥ 6
torsion subgroup: trivial
conductor (N): 17295531371
discriminant (Δ): -17295531371
Faltings height: 0.6654
naive height: 31.6585
primes of bad reduction: 17295531371
regulator: 217.50986721024661772217730063667013078584632857657
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:31:30 UTC
last updated: 2026-10-17 10:31:30 UTC

Witness: 6 independent points log in to add more points →

(-17, 119)
(-13, 120)
(-2, 99)
(5, 75)
(12, 54)
(22, 75)

Commentary

BASE records/rank_6.md#17 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:31:30 UTC · history

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